CN117233568B - Method and device for calculating carrier mobility - Google Patents
Method and device for calculating carrier mobility Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 72
- 239000004065 semiconductor Substances 0.000 claims abstract description 151
- 239000000463 material Substances 0.000 claims abstract description 149
- 238000005468 ion implantation Methods 0.000 claims abstract description 112
- 238000002513 implantation Methods 0.000 claims abstract description 106
- 238000002347 injection Methods 0.000 claims abstract description 53
- 239000007924 injection Substances 0.000 claims abstract description 53
- 238000005259 measurement Methods 0.000 claims abstract description 19
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 18
- 238000000137 annealing Methods 0.000 claims description 18
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- 238000009792 diffusion process Methods 0.000 claims description 11
- 238000004088 simulation Methods 0.000 abstract description 11
- 238000012544 monitoring process Methods 0.000 abstract description 10
- 238000004458 analytical method Methods 0.000 abstract description 4
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- XUIMIQQOPSSXEZ-UHFFFAOYSA-N Silicon Chemical compound [Si] XUIMIQQOPSSXEZ-UHFFFAOYSA-N 0.000 description 4
- 229910052710 silicon Inorganic materials 0.000 description 4
- 239000010703 silicon Substances 0.000 description 4
- XKRFYHLGVUSROY-UHFFFAOYSA-N Argon Chemical compound [Ar] XKRFYHLGVUSROY-UHFFFAOYSA-N 0.000 description 2
- IJGRMHOSHXDMSA-UHFFFAOYSA-N Atomic nitrogen Chemical compound N#N IJGRMHOSHXDMSA-UHFFFAOYSA-N 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 2
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- 229910052786 argon Inorganic materials 0.000 description 1
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Abstract
The invention discloses a method and a device for calculating carrier mobility. The method for calculating the carrier mobility comprises the following steps: performing ion implantation on the semiconductor material by adopting preset conditions; measuring the sheet resistance of the semiconductor material; determining the implantation depth and the doping concentration of ion implantation based on a Monte Carlo algorithm according to preset conditions; and calculating the carrier mobility of the semiconductor material according to the sheet resistance, the implantation depth and the doping concentration. The method not only avoids the measurement and analysis of the carrier mobility by using a professional instrument, but also saves the measurement cost of the carrier mobility. Meanwhile, the carrier mobility is measured in the monitoring of the ion implantation process, so that the carrier mobility can be calculated by multiplexing the monitoring of the ion implantation process, and the measuring cost of the carrier mobility is further reduced. Moreover, the simulation accuracy of determining the injection depth and the doping concentration of the ion injection based on the Monte Carlo algorithm according to the preset condition is relatively high, so that the measurement accuracy of the carrier mobility can be improved.
Description
Technical Field
The embodiment of the invention relates to the technical field of performance measurement of semiconductor materials, in particular to a method and a device for calculating carrier mobility.
Background
Carrier mobility is an important parameter that characterizes the conductivity properties of semiconductor materials, which is directly related to the conductivity of the semiconductor material and affects the operating speed of the semiconductor. Therefore, the method has great significance in the research and development of semiconductor materials and devices for measuring and characterizing the carrier mobility of common semiconductor materials.
In general, professional instruments are required for measuring and analyzing the carrier mobility, so that equipment cost is high, and instruments required for different materials can be different, and the cost for measuring the carrier mobility is high.
Disclosure of Invention
The invention provides a method and a device for calculating carrier mobility, which are used for measuring the carrier mobility of a semiconductor material and reducing the measuring cost of the carrier mobility.
In a first aspect, an embodiment of the present invention provides a method for calculating carrier mobility, including:
performing ion implantation on the semiconductor material by adopting preset conditions;
measuring the sheet resistance of the semiconductor material;
determining the implantation depth and the doping concentration of ion implantation based on a Monte Carlo algorithm according to the preset conditions;
and calculating the carrier mobility of the semiconductor material according to the sheet resistance, the implantation depth and the doping concentration.
Optionally, calculating carrier mobility of the semiconductor material according to the sheet resistance, the implantation depth and the doping concentration includes:
determining the relation between the sheet resistance, the injection depth and the doping concentration and the carrier mobility based on the relation between the sheet resistance and the resistivity and the injection depth and the relation between the sheet resistance and the conductivity;
and calculating the carrier mobility according to the sheet resistance, the injection depth and the doping concentration based on the relation between the sheet resistance, the injection depth and the doping concentration and the carrier mobility.
Optionally, determining the relationship between the sheet resistance, the implantation depth, and the doping concentration and the carrier mobility based on the relationship between the sheet resistance and the resistivity and the implantation depth, and the relationship between the sheet resistance and the conductivity, includes:
according to the definition of the sheet resistance, taking the vertical plane of the ion implantation surface of the semiconductor material as the cross section of the sheet resistance, and determining the relation between the sheet resistance and the resistivity and the implantation depth;
and determining the relation between the sheet resistance, the injection depth and the doping concentration and the carrier mobility based on the definition of the conductivity according to the relation that the resistivity and the conductivity are reciprocal.
Optionally, before measuring the sheet resistance of the semiconductor material, the method further comprises:
and thermally annealing the semiconductor material.
Optionally, measuring the sheet resistance of the semiconductor material includes:
four probes Fang Zuyi are used to measure the sheet resistance of the semiconductor material.
Optionally, after calculating the carrier mobility of the semiconductor material according to the sheet resistance, the implantation depth and the doping concentration, further comprising:
and calculating a carrier diffusion coefficient based on Einstein relation according to the carrier mobility.
Optionally, the preset conditions include an implanted ion species, an implantation energy, an implantation dose, and an implantation angle.
In a second aspect, an embodiment of the present invention further provides a device for calculating carrier mobility, including:
the ion implantation module is used for carrying out ion implantation on the semiconductor material by adopting preset conditions;
the measuring module is used for measuring the sheet resistance of the semiconductor material;
the determining module is used for determining the implantation depth and the doping concentration of ion implantation based on a Monte Carlo algorithm according to the preset conditions;
and the calculating module is used for calculating the carrier mobility of the semiconductor material according to the sheet resistance, the injection depth and the doping concentration.
Optionally, the computing module includes:
a relationship determining unit configured to determine a relationship between the sheet resistance, the implantation depth, and the doping concentration and the carrier mobility based on a relationship between the sheet resistance and the resistivity and the implantation depth, and a relationship between the sheet resistance and the conductivity;
and the calculating unit is used for calculating the carrier mobility according to the sheet resistance, the injection depth and the doping concentration based on the relation between the sheet resistance, the injection depth and the doping concentration and the carrier mobility.
Optionally, the relationship determination unit includes:
a first determining subunit, configured to determine, according to the definition of the sheet resistance, a relationship between the sheet resistance and the resistivity and the implantation depth by using a homeotropic surface of an ion implantation surface of the semiconductor material as a cross section of the sheet resistance;
and the second determining subunit is used for determining the relation between the sheet resistance, the injection depth and the doping concentration and the carrier mobility based on the definition of the conductivity according to the relation that the resistivity and the conductivity are reciprocal.
According to the technical scheme, when the carrier mobility of the semiconductor material is calculated, the ion implantation process of the semiconductor material can be utilized to carry out ion implantation on the semiconductor material, then the sheet resistance of the semiconductor material is measured, the implantation depth and the doping concentration of the ion implantation are determined based on a Monte Carlo algorithm according to preset conditions, and finally the carrier mobility of the semiconductor material is directly calculated according to the sheet resistance, the implantation depth and the doping concentration, so that the carrier mobility can be prevented from being measured and analyzed by a professional instrument, and the measuring cost of the carrier mobility is saved. Meanwhile, the carrier mobility can be measured in the monitoring of the ion implantation process, so that the carrier mobility can be calculated by multiplexing the monitoring of the ion implantation process, and the measuring cost of the carrier mobility is further reduced. Moreover, the simulation accuracy of determining the injection depth and the doping concentration of the ion injection based on the Monte Carlo algorithm according to the preset condition is relatively high, so that the measurement accuracy of the carrier mobility can be improved.
Drawings
Fig. 1 is a schematic flow chart of a method for calculating carrier mobility according to an embodiment of the present invention;
fig. 2 is a simulation diagram of implantation depth and doping concentration when the SRIM software performs ion implantation based on a simulation of a preset condition according to an embodiment of the present invention;
fig. 3 is a schematic flow chart of another method for calculating carrier mobility according to an embodiment of the present invention;
fig. 4 is a simulation diagram of implantation depth and doping concentration of SRIM software for simulating ion implantation of phosphorus ions based on preset conditions according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of a device for calculating carrier mobility according to an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting thereof. It should be further noted that, for convenience of description, only some, but not all of the structures related to the present invention are shown in the drawings.
Fig. 1 is a flow chart of a method for calculating carrier mobility according to an embodiment of the present invention, where the method is applicable to measuring carrier mobility of a semiconductor material during a doping process in a production process of the semiconductor material, and the method may be performed by a device for calculating carrier mobility, and specifically includes the following steps:
s110, carrying out ion implantation on the semiconductor material by adopting preset conditions;
the semiconductor material may be produced by forming a fixed material layer and doping the fixed material layer. The doping process may include diffusion and ion implantation, for example. The ion implantation process is a process of accelerating ion implantation of atoms to be doped into a solid material layer by a high-voltage electric field in a high-vacuum system, thereby selectively forming an implantation layer having specific properties in an implantation region. The ion implantation process can precisely control the concentration distribution and implantation depth of the doped ions in the solid material layer. In the ion implantation, preset conditions of the ion implantation can be set according to performance requirements of the semiconductor material, so that the ion concentration, implantation depth and the like in the semiconductor material formed after the ion implantation meet the performance requirements of the semiconductor material. Illustratively, the preset conditions may include an implanted ion species of ion implantation, implantation energy, implantation dose, and the like. The ion implantation process has low doping temperature, good implantation uniformity and small lateral diffusion, so that the ion implantation process can be used for changing the electrical property of the semiconductor material.
It should be noted that after the doping process, other film layers may be formed based on the semiconductor material, so that the semiconductor material may be used to form a semiconductor device. The ion implantation may be a one-step process for forming the semiconductor device, and the ion implantation process is multiplexed for calculating carrier mobility.
S120, measuring the sheet resistance of the semiconductor material;
wherein, after doping the semiconductor material, the sheet resistance of the semiconductor material can be measured. The sheet resistance refers to the resistance of a semiconductor material having a constant film thickness and the same length and width.
S130, determining the implantation depth and the doping concentration of ion implantation based on a Monte Carlo algorithm according to preset conditions;
after doping the semiconductor material, determining the implantation depth and the doping concentration of the ion implantation based on a Monte Carlo algorithm by adopting the same preset conditions. Illustratively, one canThe implantation depth and doping concentration of the ion implantation are determined by simulation software based on the monte carlo algorithm. For example, SRIM software may be used to simulate ion implantation processes under preset conditions, simulate various parameters of particle position, energy loss, and secondary particles, and further obtain expected values of desired physical quantities and statistical errors of phase differences. Thereby obtaining the implantation depth and the doping concentration of the ion implantation. The simulation precision of the ion implantation process under the preset condition is high through SRIM software simulation, so that the doping concentration and the implantation depth after ion implantation can be better analyzed. In addition, the SRIM software is simple to operate, and is beneficial to reducing the professional knowledge requirement of a user. In addition, the cost is lower, which is beneficial to reducing the cost of carrier mobility measurement. Fig. 2 is a simulation diagram of implantation depth and doping concentration when the SRIM software according to the embodiment of the present invention simulates ion implantation based on preset conditions. Wherein the abscissa is the implantation depth (μm), and the abscissa is the doping concentration (ions/cm) 3 ). As shown in fig. 2, under a predetermined condition of a certain ion implantation, the doping concentration of ions is different according to the implantation depth of ions. And as the implantation depth increases, the doping concentration increases with the implantation depth to reach a maximum value, and then decreases with the implantation depth.
And S140, calculating the carrier mobility of the semiconductor material according to the sheet resistance, the injection depth and the doping concentration.
After determining the sheet resistance and the implantation depth and doping concentration of ion implantation, the carrier mobility of the semiconductor material can be directly calculated according to the sheet resistance, the implantation depth and the doping concentration. The specific calculation process is as follows:
wherein Rs is the sheet resistance of the semiconductor material; q is the unit charge quantity and is 1.6E-19C;the doping concentration of the ion implantation is that r is the implantation of the ion implantationDepth of penetration (I)>Is the carrier mobility of the semiconductor material.
According to the process, when the carrier mobility of the semiconductor material is calculated, the ion implantation process of the semiconductor material can be utilized to carry out ion implantation on the semiconductor material, then the sheet resistance of the semiconductor material is measured, the implantation depth and the doping concentration of the ion implantation are determined based on the Monte Carlo algorithm according to preset conditions, and finally the carrier mobility of the semiconductor material is directly calculated according to the sheet resistance, the implantation depth and the doping concentration, so that the carrier mobility measurement and analysis by using a professional instrument can be avoided, and the carrier mobility measurement cost is saved. Meanwhile, the carrier mobility can be measured in the monitoring of the ion implantation process, so that the carrier mobility can be calculated by multiplexing the monitoring of the ion implantation process, and the measuring cost of the carrier mobility is further reduced. Moreover, the simulation accuracy of determining the injection depth and the doping concentration of the ion injection based on the Monte Carlo algorithm according to the preset condition is relatively high, so that the measurement accuracy of the carrier mobility can be improved.
On the basis of the technical scheme, the carrier mobility of the semiconductor material is calculated according to the sheet resistance, the injection depth and the doping concentration, and the method comprises the following steps:
determining the relation between the sheet resistance, the injection depth, the doping concentration and the carrier mobility based on the relation between the sheet resistance and the resistivity and the injection depth and the relation between the sheet resistance and the conductivity;
the relation between the sheet resistance and the resistivity and the implantation depth is as follows:
wherein Rs is the sheet resistance of the semiconductor material;is the resistivity of the semiconductor material; />Is a function of the implantation depth of the ion implantation with respect to the depth x of the semiconductor material.
Optionally, determining the relationship between the sheet resistance, the injection depth, the doping concentration and the carrier mobility based on the relationship between the sheet resistance and the resistivity and the injection depth, and the relationship between the sheet resistance and the conductivity comprises:
according to the definition of the sheet resistance, taking the vertical plane of the ion implantation surface of the semiconductor material as the cross section of the sheet resistance, and determining the relation between the sheet resistance and the resistivity and the implantation depth;
in the process of ion implantation, when the sheet resistance of the semiconductor material is measured, according to the definition of the sheet resistance, the vertical plane of the ion implantation surface of the semiconductor material is taken as the cross section of the sheet resistance, and at the moment, the calculation formula of the sheet resistance is as follows:
wherein Rs is the sheet resistance of the semiconductor material;is the resistivity of the semiconductor material; a is the cross section of the semiconductor material in the ion implantation direction; l is the side length of the ion implantation surface of the semiconductor material; />Is a function of the implantation depth of the ion implantation with respect to the depth x of the semiconductor material.
Illustratively, the sheet resistance of the semiconductor material can be considered as a film thickness as defined by the sheet resistanceThe resistance of the semiconductor material is L for both length and width. Therefore, according to the definition of the sheet resistance, the vertical plane of the ion implantation surface of the semiconductor material is taken as the cross section of the sheet resistance, and the relation between the sheet resistance and the resistivity and the implantation depth can be determined.
And determining the relation between the sheet resistance, the injection depth and the doping concentration and the carrier mobility based on the definition of the conductivity according to the relation that the resistivity and the conductivity are reciprocal.
Conductivity is a parameter used to describe how hard a charge flows in a substance. Conductivity is the inverse of resistivity. The resistivity is calculated as follows, according to the definition of conductivity:
wherein,is the resistivity of the semiconductor material; />Is the conductivity of the semiconductor material; />The doping concentration of ion implantation is 1.6E-19C, q is the unit charge quantity; />Is the carrier mobility of the semiconductor material.
After determining the sheet resistance of the semiconductor material, according to the relationship that the resistivity and the conductivity of the semiconductor material are reciprocal and the definition of the conductivity, the formula (1) can be determined according to the formula (3) and the formula (4), that is, the relationship of the sheet resistance, the injection depth, the doping concentration and the carrier mobility can be determined.
And calculating the carrier mobility according to the sheet resistance, the injection depth and the doping concentration based on the relation between the sheet resistance, the injection depth and the doping concentration and the carrier mobility.
Wherein, after determining the relation between the sheet resistance, the injection depth and the doping concentration and the carrier mobility, formula (1) is shown. The carrier mobility can be calculated based on the formula (1) according to the sheet resistance, the injection depth and the doping concentration, so that the measurement and analysis of the carrier mobility by using a professional instrument can be avoided, and the measurement cost of the carrier mobility is saved. Meanwhile, the carrier mobility can be measured in the monitoring of the ion implantation process, so that the carrier mobility can be calculated by multiplexing the monitoring of the ion implantation process, and the measuring cost of the carrier mobility is further reduced. Moreover, the simulation accuracy of determining the injection depth and the doping concentration of the ion injection based on the Monte Carlo algorithm according to the preset condition is relatively high, so that the measurement accuracy of the carrier mobility can be improved.
Fig. 3 is a flow chart of another method for calculating carrier mobility according to an embodiment of the present invention, as shown in fig. 3, the method includes:
s210, carrying out ion implantation on the semiconductor material by adopting preset conditions;
s220, performing thermal annealing on the semiconductor material.
Among other things, the thermal anneal may employ a rapid thermal processing (rapid thermal processing, RTP) process. After the ion implantation process, a damaged area is formed on the solid material layer, and most of implanted ions are positioned at lattice gap positions and have no electric activity; to reduce defect density and allow interstitial impurity ions to migrate to lattice sites making them electroactive, an annealing process is typically used for repair. The thermal annealing process principle is to utilize heat energy to carry out heat treatment on the sample after ion implantation so as to eliminate damage, activate implantation of impurity ions and restore the electrical property of crystals in the solid material layer. The rapid heat treatment can heat the solid material layer to the temperature required by annealing in a very short time through a very rapid temperature rising rate, so that internal defects in the solid material layer are eliminated, and the performance of the semiconductor material is improved. And the RTP process has extremely high temperature control precision and temperature uniformity, and can ensure the performance of the semiconductor material after thermal annealing. Illustratively, the annealing temperature using the RTP process may be 700-1900 deg.C, and the annealing time may be 5-300 s, with the annealing atmosphere including, but not limited to, nitrogen and argon.
S230, measuring the sheet resistance of the semiconductor material;
s240, determining the implantation depth and the doping concentration of ion implantation based on a Monte Carlo algorithm according to preset conditions;
s250, calculating the carrier mobility of the semiconductor material according to the sheet resistance, the injection depth and the doping concentration.
Based on the above technical solutions, the method for measuring the sheet resistance of the semiconductor material includes:
four probes Fang Zuyi are used to measure the sheet resistance of the semiconductor material.
The four probes Fang Zuyi measure the sheet resistance, i.e., the sheet resistance, of the semiconductor material after the ion implantation process. The ratio of the bias voltage to the current in the current flowing direction is the square resistance, and the square resistance can be obtained by measuring the voltage and the current between the four probes through the four probes Fang Zuyi. The square resistance of the semiconductor material is measured by adopting the four probes Fang Zuyi, so that the square resistance and the uniformity of the semiconductor material can be monitored, and the implantation uniformity of the ion implantation process can be monitored. Meanwhile, the measured sheet resistance value can be reused for calculating the carrier mobility, so that the measuring cost of the carrier mobility can be further reduced.
On the basis of the technical schemes, the preset conditions comprise the ion implantation type, implantation energy, implantation dosage and implantation angle.
In particular, the preset conditions may include various parameters of the ion implantation process. The implanted ion species may be set according to the performance requirements of the semiconductor material. Illustratively, the implanted ion species may include at least one of B, al, in, N, P, as and Sb. The implantation energy may determine the implantation depth of the ions. The implantation energy may be, for example, 1 to 1000Kev. The implant dose may determine the doping concentration of the ions. Exemplary implant doses may be 1E 13-1E 17ions/cm 2 . When semiconductor materials are used to form semiconductor devices, the implantation angle may be effective to improve the channeling of the semiconductor devices. Illustratively, the implantation angle may be 0-60 °. In the ion implantation process, the performance of the semiconductor material after the ion implantation process can meet the requirements by setting the process parameters such as the ion implantation type, implantation energy, implantation dosage, implantation angle and the like.
The ion implantation with phosphorus ions and the calculation of carrier mobility are exemplified below. The specific process is as follows:
and (3) selecting a silicon wafer for phosphorus ion implantation, wherein the preset condition can be that the implantation energy is 100Kev, the implantation dosage is 1E13ions/cm < 2 >, and the implantation angle is 7 degrees. After the ion implantation process is finished, rapid thermal annealing is carried out by adopting an RTP process, the annealing temperature is 925 ℃, the annealing time is 15s, and the annealing atmosphere is Ar. Then, the sheet resistance was measured by four probes Fang Zuyi to be 1602 Ω/≡. Then simulating phosphorus ion implantation into the silicon wafer by using SRIM software, wherein the implantation energy is 100Kev, the implantation dosage is 1E13ions/cm < 2 >, and the implantation angle is 7 degrees. Fig. 4 is a simulation diagram of implantation depth and doping concentration of SRIM software for simulating ion implantation of phosphorus ions based on preset conditions according to an embodiment of the present invention. Wherein the abscissa is the implantation depth (μm), and the abscissa is the doping concentration (ions/cm) 3 ). As shown in FIG. 4, under the above-mentioned preset conditions, the implantation depth of the phosphorus ions is 0.16um, and the doping concentration is 8.76E17ions/cm 3 . Thereby the carrier mobility of 277.97cm can be calculated according to the formula (1) according to the sheet resistance, the injection depth and the doping concentration 2 /V.s。
On the basis of the above technical solutions, after calculating the carrier mobility of the semiconductor material according to the sheet resistance, the injection depth and the doping concentration, the method further includes:
the carrier diffusion coefficient is calculated based on the einstein relation from the carrier mobility.
Wherein, the Einstein relation of the diffusion coefficient and the carrier mobility is as follows:
wherein,carrier mobility for semiconductor materials; />Is Boltzmann constant 1.380649E-23J/K; t is room temperature 300K; q is the unit charge quantity and is 1.6E-19C; />Is the diffusion coefficient of the carrier.
After determining the carrier mobility, the diffusion coefficient of the carrier can be calculated from the einstein relation. For example, with continued reference to the above embodiment, a silicon wafer is selected for phosphorus ion implantation, where the preset condition may be an implantation energy of 100Kev, an implantation dose of 1E13ions/cm2, and an implantation angle of 7 °. After the ion implantation process is finished, rapid thermal annealing is carried out by adopting an RTP process, the annealing temperature is 925 ℃, the annealing time is 15s, and the annealing atmosphere is Ar. Then, the sheet resistance was measured by four probes Fang Zuyi to be 1602 Ω/≡. Then simulating phosphorus ion implantation into the silicon wafer by using SRIM software, wherein the implantation energy is 100Kev, the implantation dosage is 1E13ions/cm < 2 >, and the implantation angle is 7 degrees. Under the preset condition, the implantation depth of the phosphorus ions is 0.16um, and the doping concentration is 8.76E17ions/cm 3 . According to the square resistance, the injection depth and the doping concentration, the carrier mobility is 277.97cm calculated according to the formula (1) 2 and/V.s. Then, the carrier diffusion coefficient at room temperature was calculated to be 7.19cm according to the formula (5) 2 /s。
The embodiment of the invention also provides a device for calculating the carrier mobility. Fig. 5 is a schematic structural diagram of a device for calculating carrier mobility according to an embodiment of the present invention. As shown in fig. 5, the carrier mobility calculating device includes:
an ion implantation module 10 for performing ion implantation of the semiconductor material using preset conditions;
a measuring module 20 for measuring the sheet resistance of the semiconductor material;
a determining module 30, configured to determine an implantation depth and a doping concentration of the ion implantation based on a monte carlo algorithm according to a preset condition;
a calculation module 40 for calculating carrier mobility of the semiconductor material according to the sheet resistance, the implantation depth and the doping concentration.
According to the technical scheme, when the carrier mobility of the semiconductor material is calculated, the ion implantation process of the semiconductor material is utilized by the ion implantation module to carry out ion implantation on the semiconductor material, then the sheet resistance of the semiconductor material is measured by the measurement module, the implantation depth and the doping concentration of the ion implantation are determined by the determination module according to the preset condition based on the Monte Carlo algorithm, and finally the carrier mobility of the semiconductor material is directly calculated by the calculation module according to the sheet resistance, the implantation depth and the doping concentration, so that the measurement and analysis of the carrier mobility by using a professional instrument can be avoided, and the measurement cost of the carrier mobility is saved. Meanwhile, the carrier mobility can be measured in the monitoring of the ion implantation process, so that the carrier mobility can be calculated by multiplexing the monitoring of the ion implantation process, and the measuring cost of the carrier mobility is further reduced. Moreover, the simulation accuracy of determining the injection depth and the doping concentration of the ion injection based on the Monte Carlo algorithm according to the preset condition is relatively high, so that the measurement accuracy of the carrier mobility can be improved.
On the basis of the technical scheme, the preset conditions comprise the ion implantation type, implantation energy, implantation dosage and implantation angle.
On the basis of the technical schemes, the calculation module comprises:
the relation determining unit is used for determining the relation between the square resistance, the injection depth, the doping concentration and the carrier mobility based on the relation between the square resistance, the resistivity and the injection depth and the relation between the square resistance and the conductivity;
and the calculating unit is used for calculating the carrier mobility according to the sheet resistance, the injection depth and the doping concentration based on the relation between the sheet resistance, the injection depth and the doping concentration and the carrier mobility.
On the basis of the above technical solutions, the relationship determining unit includes:
the first determining subunit is used for determining the relation between the square resistance, the resistivity and the implantation depth by taking the vertical plane of the ion implantation surface of the semiconductor material as the cross section of the square resistance according to the definition of the square resistance;
and the second determining subunit is used for determining the relation of the sheet resistance, the injection depth and the doping concentration and the carrier mobility based on the definition of the conductivity according to the relation of the resistivity and the conductivity which are reciprocal.
On the basis of the above technical solutions, the device for calculating carrier mobility further includes:
and the thermal annealing module is used for carrying out thermal annealing on the semiconductor material before the measuring module measures the sheet resistance of the semiconductor material.
Based on the above technical solutions, the measurement module includes four probes Fang Zuyi, so that when the measurement module measures the sheet resistance of the semiconductor material, the four probes Fang Zuyi are used to measure the sheet resistance of the semiconductor material.
The square resistance of the semiconductor material is measured by adopting the four probes Fang Zuyi, so that the square resistance and the uniformity of the semiconductor material can be monitored, and the implantation uniformity of the ion implantation process can be monitored. Meanwhile, the measured sheet resistance value can be reused for calculating the carrier mobility, so that the measuring cost of the carrier mobility can be further reduced.
On the basis of the above technical solutions, the device for calculating carrier mobility further includes:
the diffusion coefficient calculation module is used for calculating carrier mobility of the semiconductor material according to the sheet resistance, the injection depth and the doping concentration, and then calculating carrier diffusion coefficients based on Einstein relation according to the carrier mobility.
Note that the above is only a preferred embodiment of the present invention and the technical principle applied. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, while the invention has been described in connection with the above embodiments, the invention is not limited to the embodiments, but may be embodied in many other equivalent forms without departing from the spirit or scope of the invention, which is set forth in the following claims.
Claims (5)
1. A method for calculating carrier mobility, comprising:
performing ion implantation on the semiconductor material by adopting preset conditions;
measuring the sheet resistance of the semiconductor material; the cross section of the sheet resistor is a vertical plane of the ion implantation surface of the semiconductor material;
determining the implantation depth and the doping concentration of ion implantation based on a Monte Carlo algorithm according to the preset conditions;
calculating carrier mobility of the semiconductor material according to the sheet resistance, the injection depth and the doping concentration; the specific calculation process is as follows:
wherein Rs is the sheet resistance of the semiconductor material; q is the unit charge quantity and is 1.6E-19C; />The doping concentration of the ion implantation is r is the implantation depth of the ion implantation, +.>Carrier mobility for semiconductor materials;
calculating carrier mobility of the semiconductor material from the sheet resistance, the implantation depth, and the doping concentration, comprising:
determining the relation between the sheet resistance, the injection depth and the doping concentration and the carrier mobility based on the relation between the sheet resistance and the resistivity and the injection depth and the relation between the sheet resistance and the conductivity; wherein the sheet resistance is related to the resistivity and the implantation depth as follows:
wherein Rs is the sheet resistance of the semiconductor material; />Is the resistivity of the semiconductor material; />An implantation depth x function of ion implantation with respect to a depth of the semiconductor material;
calculating the carrier mobility according to the sheet resistance, the injection depth and the doping concentration based on the relation between the sheet resistance, the injection depth and the doping concentration and the carrier mobility;
measuring a sheet resistance of the semiconductor material, comprising:
measuring the sheet resistance of the semiconductor material with four probes Fang Zuyi;
determining the relationship of the sheet resistance, the injection depth, and the doping concentration to the carrier mobility based on the relationship of the sheet resistance to the resistivity and the injection depth, and the relationship of the sheet resistance to the conductivity, comprising:
according to the definition of the sheet resistance, taking the vertical plane of the ion implantation surface of the semiconductor material as the cross section of the sheet resistance, and determining the relation between the sheet resistance and the resistivity and the implantation depth; the calculation formula of the sheet resistance is as follows:
wherein Rs is the sheet resistance of the semiconductor material; />Is the resistivity of the semiconductor material; a is the cross section of the semiconductor material in the ion implantation direction; l is the side length of the ion implantation surface of the semiconductor material; />An implantation depth x function of ion implantation with respect to a depth of the semiconductor material;
determining the relation of the sheet resistance, the injection depth and the doping concentration and the carrier mobility based on the definition of the conductivity according to the relation that the resistivity and the conductivity are reciprocal; the calculation formula of the resistivity is as follows:
wherein (1)>Is the resistivity of the semiconductor material; />Is the conductivity of the semiconductor material; />The doping concentration of ion implantation is 1.6E-19C, q is the unit charge quantity; />Is the carrier mobility of the semiconductor material.
2. The method of calculating carrier mobility according to claim 1, further comprising, before measuring the sheet resistance of the semiconductor material:
and thermally annealing the semiconductor material.
3. The method according to claim 1, characterized by further comprising, after calculating the carrier mobility of the semiconductor material from the sheet resistance, the injection depth, and the doping concentration:
and calculating a carrier diffusion coefficient based on Einstein relation according to the carrier mobility.
4. The method according to claim 1, wherein the preset conditions include an ion species to be implanted, an implantation energy, an implantation dose, and an implantation angle.
5. A carrier mobility calculation device, comprising:
the ion implantation module is used for carrying out ion implantation on the semiconductor material by adopting preset conditions;
a measurement module for measuring the sheet resistance of the semiconductor material using four probes Fang Zuyi; the cross section of the sheet resistor is a vertical plane of the ion implantation surface of the semiconductor material;
the determining module is used for determining the implantation depth and the doping concentration of ion implantation based on a Monte Carlo algorithm according to the preset conditions;
a calculation module for calculating carrier mobility of the semiconductor material according to the sheet resistance, the injection depth and the doping concentration; the specific calculation process is as follows:
wherein Rs is the sheet resistance of the semiconductor material; q is the unit charge quantity and is 1.6E-19C; />The doping concentration of the ion implantation is r is the implantation depth of the ion implantation, +.>Carrier mobility for semiconductor materials;
the computing module includes:
a relationship determining unit configured to determine a relationship between the sheet resistance, the implantation depth, and the doping concentration and the carrier mobility based on a relationship between the sheet resistance and the resistivity and the implantation depth, and a relationship between the sheet resistance and the conductivity; wherein the sheet resistance is related to the resistivity and the implantation depth as follows:
wherein Rs is the sheet resistance of the semiconductor material; />Is the resistivity of the semiconductor material; />An implantation depth x function of ion implantation with respect to a depth of the semiconductor material;
a calculation unit configured to calculate the carrier mobility from the sheet resistance, the injection depth, and the doping concentration based on the relationship between the sheet resistance, the injection depth, and the doping concentration and the carrier mobility;
the relationship determination unit includes:
a first determining subunit, configured to determine, according to the definition of the sheet resistance, a relationship between the sheet resistance and the resistivity and the implantation depth by using a homeotropic surface of an ion implantation surface of the semiconductor material as a cross section of the sheet resistance; the calculation formula of the sheet resistance is as follows:
wherein Rs is the sheet resistance of the semiconductor material; />Is the resistivity of the semiconductor material; a is the cross section of the semiconductor material in the ion implantation direction; l is the side length of the ion implantation surface of the semiconductor material; />An implantation depth x function of ion implantation with respect to a depth of the semiconductor material;
a second determining subunit configured to determine, based on the definition of the conductivity, a relationship between the sheet resistance, the implantation depth, and the doping concentration and the carrier mobility according to a relationship in which the resistivity and the conductivity are reciprocal; the calculation formula of the resistivity is as follows:
wherein (1)>Is the resistivity of the semiconductor material; />Is the conductivity of the semiconductor material; />The doping concentration of ion implantation is 1.6E-19C, q is the unit charge quantity; />Is the carrier mobility of the semiconductor material.
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